Sex differences in weight gain (original Lord formulation)

Variables

  • weight time 1
  • weight time 2
  • weight change
  • sex

Issues

  • t-test on change vs. ancova
  • Statistician 1 concludes no difference in change
  • Statistician 2 concludes a difference in time 2 if controlling for time 1

Results

  • Both statisticians are correct
  • t-test on change = total effect
  • ancova = direct effect

DAG

Indirect effect: is a*c

Direct effect: b

Total effect: b + a*c - a

Treatment with confounding (Wainer & Brown)

Variables

  • weight time 1
  • weight time 2
  • weight change
  • table A vs. B

Issues

  • Heavier kids more likely to sit at table B
  • Two statisticians come the conclusions as before

Results

  • Weight time 1 is now a confounder
  • Arrow from time 1 to ‘treatment’
  • Statistician 1 is incorrect because they do not adjust
  • Statistician 2

Birth Weight Paradox

Variables

  • birthweight
  • smoking mom
  • infant mortality

Issues

  • No difference score
  • Before, focus on clash between two seemingly legitimate methods of analysis
  • Now using ancova but results seem implausible

Results

  • low birthweight children have higher mortality rate (100 fold higher)
  • children of smoking mothers notably more likely to have low birghtweight
  • low birthweight children born to smoking mothers have a lower mortality rate
  • Conclusion: expectant mothers should start smoking!

Results

Collider bias (explain away effect)